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Perimeter Problem

Perimeter Problem
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2017-01-05 16:37
PolygonTransformationGeometric Construction
This example demonstrates how to solve perimeter problems through geometric construction. Key mathematical concepts include geometric construction, quadrilaterals (kite, trapezoid), and fractal geometry. Using GeoGebra commands such as Circle, Point, OrthogonalLine, and Intersect, complex geometric shapes can be constructed. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, p) → c_1
  2. Point(c_1) → B
  3. OrthogonalLine(B, Segment[A, B]) → f
  4. Circle(B, q) → c_2
  5. Intersect(c_2, f, 2) → C
  6. Line(A, f) → g
  7. OrthogonalLine(C, f) → h
  8. Intersect(g, h) → D
  9. Polygon(A, B, C, D) → poly1, a, b, c, d
  10. Circle(E, r) → e_1
  11. Point(e_1) → F
  12. OrthogonalLine(F, Segment[E, F]) → i
  13. Circle(F, s) → e_2
  14. Intersect(e_2, i, 2) → G
  15. Line(E, i) → j
  16. OrthogonalLine(G, i) → k
  17. Intersect(j, k) → H
  18. Polygon(E, F, G, H) → poly2, l, m, n, o
  19. Segment(I_1, J_1) → f_1
  20. Segment(I_2, J_2) → f_2
  21. Segment(I_3, J_3) → f_3
  22. Segment(K_1, L_1) → g_1
  23. Point(Circle[I, 8]) → J
  24. Point(Circle[Q, 5]) → R
  25. Polygon(Q, R, S, T, U, V, W, Z) → poly3, q_1, r_1, s_1, t_2, u_1, v_1, w, z_1
  26. Segment((x(P_1), y(P_1) - (u * 3.75 / 2)), (x(P_1), y(P_1) + (u * 3.75 / 2))) → t
  27. Segment((x(P_2), y(P_2) - (u * 3.75 / 2)), (x(P_2), y(P_2) + (u * 3.75 / 2))) → t_1
  28. Segment((x(Q_2) - (u * 5.5 / 2), y(Q_2)), (x(Q_2) + (u * 5.5 / 2), y(Q_2))) → e_3
  29. Segment((x(Q_1) - (u * 5.5 / 2), y(Q_1)), (x(Q_1) + (u * 5.5 / 2), y(Q_1))) → e